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作者：Rudelson, Mark; Samorodnitsky, Alex; Zeitouni, Ofer
作者单位：University of Michigan System; University of Michigan; Hebrew University of Jerusalem; Weizmann Institute of Science; New York University
摘要：We analyze the behavior of the Barvinok estimator of the hafnian of even dimension, symmetric matrices with nonnegative entries. We introduce a condition under which the Barvinok estimator achieves subexponential errors, and show that this condition is almost optimal. Using that hafnians count the number of perfect matchings in graphs, we conclude that Barvinok's estimator gives a polynomial-time algorithm for the approximate (up to subexponential errors) evaluation of the number of perfect ma...
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作者：Mastrolia, Thibaut; Possamai, Dylan; Reveillac, Anthony
作者单位：Universite PSL; Universite Paris-Dauphine; Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse
摘要：In this paper, we study the existence of densities (with respect to the Lebesgue measure) for marginal laws of the solution (Y, Z) to a quadratic growth BSDE. Using the (by now) well-established connection between these equations and their associated semi-linear PDEs, together with the Nourdin-Viens formula, we provide estimates on these densities.
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作者：Baudoin, F.; Nualart, E.; Ouyang, C.; Tindel, S.
作者单位：Purdue University System; Purdue University; Pompeu Fabra University; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Universite de Lorraine
摘要：This article investigates several properties related to densities of solutions (X-t)(t is an element of[0,1]) to differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/4. We first determine conditions for strict positivity of the density of X-t. Then we obtain some exponential bounds for this density when the diffusion coefficient satisfies an elliptic type condition. Finally, still in the elliptic case, we derive some bounds on the hitting probabilities of se...
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作者：Berger, Noam; Cohen, Moran; Rosenthal, Ron
作者单位：Hebrew University of Jerusalem; Technical University of Munich; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：In this work, we discuss certain ballistic random walks in random environments on Z(d), and prove the equivalence between the static and dynamic points of view in dimension d >= 4. Using this equivalence, we also prove a version of a local limit theorem which relates the local behavior of the quenched and annealed measures of the random walk by a prefactor.
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作者：Bandeira, Afonso S.; van Handel, Ramon
作者单位：Princeton University; Princeton University
摘要：This bound is optimal in the sense that a matching lower bound holds under mild assumptions, and the constants are sufficiently sharp that we can often capture the precise edge of the spectrum. Analogous results are obtained for rectangular matrices and for more general sub-Gaussian or heavy-tailed distributions of the entries, and we derive tail bounds in addition to bounds on the expected norm. The proofs are based on a combination of the moment method and geometric functional analysis techn...
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作者：Flandoli, Franco; Zanco, Giovanni
作者单位：University of Pisa
摘要：In this paper, a Banach space framework is introduced in order to deal with finite-dimensional path-dependent stochastic differential equations. A version of Kolmogorov backward equation is formulated and solved both in the space of LP paths and in the space of continuous paths using the associated stochastic differential equation, thus establishing a relation between path-dependent SDEs and PDEs in analogy with the classical case. Finally, it is shown how to establish a connection between suc...
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作者：Puhalskii, Anatolii A.
摘要：We consider two Ito equations that evolve on different time scales. The equations are fully coupled in the sense that all of the coefficients may depend on both the slow and the fast variables and the diffusion terms may be correlated. The diffusion term in the slow process is small. A large deviation principle is obtained for the joint distribution of the slow process and of the empirical process of the fast variable. By projecting on the slow and fast variables, we arrive at new results on l...
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作者：Cebron, Guillaume
作者单位：Saarland University
摘要：This paper investigates homomorphisms a la Bercovici-Pata between additive and multiplicative convolutions. We also consider their matricial versions which are associated with measures on the space of Hermitian matrices and on the unitary group. The previous results combined with a matricial model of Benaych-Georges and Cabanal-Duvillard allow us to define and study the large N limit of a new matricial model on the unitary group for free multiplicative Levy processes.
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作者：Garban, Christophe; Rhodes, Remi; Vargas, Vincent
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：We construct a stochastic process, called the Liouville Brownian motion, which is the Brownian motion associated to the metric e(gamma X(z)) dz(2), gamma < gamma(c) = 2 and X is a Gaussian Free Field. Such a process is conjectured to be related to the scaling limit of random walks on large planar maps eventually weighted by a model of statistical physics which are embedded in the Euclidean plane or in the sphere in a conformal manner. The construction amounts to changing the speed of a standar...
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作者：Cerrai, Sandra; Salins, Michael
作者单位：University System of Maryland; University of Maryland College Park
摘要：In this paper, we study the quasi-potential for a general class of damped semilinear stochastic wave equations. We show that as the density of the mass converges to zero, the infimum of the quasi-potential with respect to all possible velocities converges to the quasi-potential of the corresponding stochastic heat equation, that one obtains from the zero mass limit. This shows in particular that the Smoluchowski Kramers approximation is not only valid for small time, but in the zero noise limi...
